You must have at least 32MB of memory and 110MB of hard disk space. For a minimal console-based system (all standard packages), 250MB is required. If you want to install a reasonable amount of software, including the X Window System, and some development programs and libraries, you'll need at least 400MB. For a more or less complete installation, you'll need around 800MB. To install everything available in Debian, you'll probably need around 6 GB. Actually, installing everything doesn't even make sense, since some packages conflict with others.
On the Amiga the size of FastRAM is relevant towards the total memory requirements. Also, using Zorro cards with 16-bit RAM is not supported; you'll need 32-bit RAM. The amiboot program can be used to disable 16-bit RAM; see the Linux/m68k FAQ. Recent kernels should disable 16-bit RAM automatically.
On the Atari, both ST-RAM and Fast RAM (TT-RAM) are used by Linux. Many users have reported problems running the kernel itself in Fast RAM, so the Atari bootstrap will place the kernel in ST-RAM. The minimum requirement for ST-RAM is 2 MB.
On the Macintosh, care should be taken on machines with RAM-based video (RBV). The RAM segment at physical address 0 is used as screen memory, making the default load position for the kernel unavailable. The alternate RAM segment used for kernel and RAMdisk must be at least 4 MB.